Follow below steps:
The location of the oil tanker and the luxury liner at time t hours after 2 p.m.:
The oil tanker's location: (-14t, 0)
The luxury liner's location: (0, 16t)
The distance d between the oil tanker and the luxury liner at time t:
The distance formula = √((-14t - 0)^2 + (0 - 16t)^2) = √(196t^2 + 256t^2) = √(452t^2) = 2√(113)t
The distance d between the oil tanker and the luxury liner at that time is [tex]\( \sqrt{452} \cdot t \)[/tex] kilometers.
To solve this problem, we'll use the concepts of distance, speed, and coordinate geometry.
Let ( t ) be the number of hours after 2 p.m.
Location of the Oil Tanker:
At ( t ) hours after 2 p.m., the oil tanker has traveled ( 14t ) kilometers west from the origin.
So, its location is (-14t, 0) .
Location of the Luxury Liner:*
At ( t ) hours after 2 p.m., the luxury liner has traveled ( 16t ) kilometers north from the origin.
So, its location is (0, 16t).
Distance between the Oil Tanker and the Luxury Liner:
We'll use the distance formula: [tex]\( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \).[/tex]
[tex]\[ d = \sqrt{(-14t - 0)^2 + (0 - 16t)^2} \][/tex]
[tex]\[ d = \sqrt{(-14t)^2 + (-16t)^2} \][/tex]
[tex]\[ d = \sqrt{196t^2 + 256t^2} \][/tex]
[tex]\[ d = \sqrt{452t^2} \][/tex]
[tex]\[ d = \sqrt{452} \cdot t \][/tex]
So, the location of the oil tanker is [tex]\( (-14t, 0) \)[/tex], the location of the luxury liner is [tex]\( (0, 16t) \)[/tex], and the distance between them at ( t ) hours after 2 p.m. is [tex]\( \sqrt{452} \cdot t \)[/tex] kilometers.
All of the following expressions represent the sum of n and itself, except _____.
n + n
2n
n²
Answer: [tex]n^{2}[/tex]
Step-by-step explanation:
(n + n) represents the definition of the sum of n and itself.
(2n) means two times n, wich is the same as adding n + n.
[tex]n^{2}[/tex] actually represents the multiplication of n two times: [tex]n*n[/tex]
For example, if n=3:
[tex]n+n=3+3=6[/tex]
[tex]2n=2(3)=6[/tex]
[tex]n^{2}=3^{2} =9[/tex]
Which equation has no solution?
A) 2.3y + 2 + 3.1y = 4.3y + 1.6 + 1.1y + 0.4
B) 32x + 25 - 21x = 10x
C) 5/8 x + 2.5 = 3/8 x + 1.5 + 1/4 x
D) 1/3 + 1/7 y = 3/7 y
PLEASE HELP!!
| THANK YOU SO MUCH |
Answer: c
Step-by-step explanation:
Determine the effective rate for $1 for 1 year at 5.9% compounded quarterly.
if y varies directly as x and y=6 when x =-7, find y when x is 4
When x is 4, y is approximately -3.43.
Explanation:To find y when x is 4, we can use the given information that y varies directly as x. This means that the ratio of y to x remains constant. We can set up a proportion using the initial values of y and x and solve for the unknown value:
6 / -7 = y / 4
By cross-multiplying, we get y = -24 / 7. Therefore, when x is 4, y is approximately -3.43.
Learn more about Direct Variation here:https://brainly.com/question/34355670
#SPJ11
a few questions i need help with.
Is the subset w = {(x, y, z) | z = 1} ⊂ r 3 a vector subspace of r 3 ? explain why or why not?
what is the value of the 7 equal to (7×1/100)
Determine whether the variable is qualitative or quantitative. explain your reasoning. miles per gallon that a car gets for highway driving
When mary began her trip from san jose to la, she filled her car's tank with gas and reset its trip meter to zero. after traveling 324 miles, she stopped at a gas station to refuel; the gas tank required 17 gallons. mary wants a program that calculates and displays her car's gas mileage at any time during the trip. the gas mileage is the number of miles her car was driven per gallon of gas?
To calculate Mary's car's gas mileage, divide the number of miles driven by the number of gallons of gas used. In this scenario, her car's gas mileage is approximately 19.06 miles per gallon.
Explanation:To calculate Mary's car's gas mileage, we need to divide the number of miles driven by the number of gallons of gas used. In this scenario, Mary traveled 324 miles and used 17 gallons of gas. Therefore, her car's gas mileage can be calculated as:
Gas mileage = Miles driven / Gallons of gas used
Substituting the values:
Gas mileage = 324 miles / 17 gallons
Simplifying the equation:
Gas mileage = 19.06 miles per gallon (rounded to two decimal places)
Learn more about Gas Mileage here:https://brainly.com/question/33812030
#SPJ2
a pump is running at 6.4 quarts per minute. how many gallons per hour is this?
If Mr. Khans buys 15 staplers, it would cost him $254.85. How would you write this using function notation?
Answer:
f(x) = don't spend more than 200 dollars on staplers
Step-by-step explanation:
Ignore the bottom...the top question is what I’m struggling with
Joanne is depositing money into a bank account. After 3 months there is $150 in the account. After 6 months there is $300 in the account. Determine the constant rate of change of the account.
Answer:
The constant rate of change of the account is $50 or Increasing by $50 per month.
Step-by-step explanation:
Consider the provided information.
Joanne is depositing money into a bank account. After 3 months there is $150 in the account. After 6 months there is $300 in the account.
Rate of change is known as how one quantity change in relation to other.
The rate of change can be calculated as:
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Now use the above formula to calculated the rate of change.
[tex]\frac{300-150}{6-3}[/tex]
[tex]\frac{150}{3}[/tex]
[tex]50[/tex]
Hence, the constant rate of change of the account is $50 or Increasing by $50 per month.
an airplane approaching its destination has begun it's final descent into the airport. if the plane descends at a rate of 300 feet per minute. what is the change in altitude of the plane after 4 minutes?
In order to start a business, a student takes out a simple interest loan for $7000.00 for 6 months at a rate of 8.00 %
an equation is shown below. 3x-10x+5=5x+17 what is the value of x that makes the equation true?
collect like terms;
3x-10x=-7x
-7x+5=5x+17
move the variable to the left and change sign
-7x+5=5x+17
move the constant to the right and change sign
-7x-5x+17-5
collect the like terms
-12x=17-5
subtract the numbers
-12x=12
divide both sides by -12
your answer is: x= -1
which number is greater 67.89 and 67.98
3x + 5x = 10 Which problem requires the same strategy (combining like terms)?
Solve: 5x - 7x + 6 = -2(x - 3).
A)
0
B)
3
4
C)
2
D)
infinitely many solutions
Answer:
D) infinitely many solutions
Step-by-step explanation:
The equation reduces to ...
-2x +6 = -2x +6
This is true for all possible values of x, so there are infinitely many solutions.
Kurt and Maria’s high school is having a newspaper drive.The goal is to collect 3,585 pounds of newspapers. So far, 21% of the goal has been reached. Kurt estimated the number of pounds of newspapers collected by finding 10% of 3,600 and then multiplying the result by 2. Maria estimated the number of pounds of newspapers collected by finding mc006-1.jpg of 3,600. Who is right, and why?
the 4th and 13th terms of an AP are 5 and -1, find the 8th term of an AP
A gas station operates two pumps, each of which can pump up to 10,000 gallons of gas in a month. the total of gas pumped at the station in a month is a random variable y (measured in 10,000 gallons) with a probability density function (p.d.f.) given by compute e(y)
The expected value E(y) cannot be computed without the given probability density function for the random variable y. The computation involves integrating the product of the variable and its probability density over its range. An example has been provided for how to compute the expected value with a hypothetical p.d.f.
Explanation:To answer the student's question, it appears there may be a missing probability density function (p.d.f.) for the random variable y, which represents the total amount of gas pumped at the station in a month. Without the actual function, we cannot compute E(y), which is the expected value (mean) of the random variable y. In general, if we had the p.d.f., we would compute the expected value by integrating the product of the variable and its probability density over its range.
An example of how to compute the expected value if we had a p.d.f. f(y) might look like this:
E(y) = ∫ y × f(y) dy
For instance, if the p.d.f. were f(y) = ay (a being a constant) over the interval [0, 1], then:
Integrate the product of y and the p.d.f. over the interval:E(y) = ∫01 y × ay dy = a × ∫01 y² dyAfter computing the integral you would find the expected value E(y).However, without the p.d.f. provided, we can only state the method, not the actual expected value.
Learn more about Expected Value here:https://brainly.com/question/37190983
#SPJ3
if tanx=-4/3 and x is in quadrant 2 then cos2x=?
A. 7/25
b. -3/5
c. -7/25
d. 3/5
Trigonometric Identities are equalities that utilize trigonometry functions and hold true for all variables in the equation. The correct option is C, -7/25.
What are Trigonometric Identities?Trigonometric Identities are equalities that utilize trigonometry functions and hold true for all variables in the equation. There are several trigonometric identities relating to the side length and angle of a triangle.
Given that the value of tan(x) = -4/3 and x is in quadrant 2.
In order to find the value of cos(2x), we can use the trigonometric identity of cos(2x), therefore, for cos(2x) we can write,
[tex]\cos(2x) = \dfrac{1-\tan^2(x)}{1+\tan^2(x)}[/tex]
Since the value of tan(x) is known, substitute the value in the identity,
[tex]\cos(2x) = \dfrac{1-(-\frac{4}{3})^2}{1+(-\frac{4}{3})^2}\\\\\cos(2x) = \dfrac{1-(\frac{16}{9})}{1+(\frac{16}{9})}\\\\[/tex]
cos(2x) = (-7/9) × (9/25)
Cancelling 9 from the numerator and the denominator,
cos(2x) = -7/25
Hence, if tanx=-4/3 and x are in quadrant 2 then cos2x=-7/25.
Learn more about Trigonometric Identities:
https://brainly.com/question/13094664
#SPJ2
The correct answer is c. [tex]$\cos(2x) = -\frac{7}{25}$[/tex].
First, we find [tex]$\sin(x)$[/tex] and [tex]$\cos(x)$[/tex] using the given value of [tex]$\tan(x)$[/tex]:
[tex]$\tan(x) = \frac{\sin(x)}{\cos(x)} = -\frac{4}{3}$.[/tex]
We can use the Pythagorean identity [tex]$\sin^2(x) + \cos^2(x) = 1$[/tex] to find [tex]$\sin(x)$[/tex] and [tex]$\cos(x)$[/tex]. Let's assume [tex]$\sin(x) = \frac{4}{5}$[/tex] (since [tex]$\tan(x) = -\frac{4}{3}$[/tex], and we are looking for a positive value of [tex]$\sin(x)$[/tex] in quadrant 2). Using the Pythagorean identity:
[tex]$\left(\frac{4}{5}\right)^2 + \cos^2(x) = 1$ \\ $\frac{16}{25} + \cos^2(x) = 1$ \\ $\cos^2(x) = 1 - \frac{16}{25}$ \\ $\cos^2(x) = \frac{25}{25} - \frac{16}{25}$ \\ $\cos^2(x) = \frac{9}{25}$. \\[/tex]
Since [tex]$\cos(x)$[/tex] is negative in quadrant 2, we have [tex]$\cos(x) = -\frac{3}{5}$[/tex].
Now, we can use the double-angle formula for cosine:
[tex]$\cos(2x) = 2\cos^2(x) - 1$ \\ $\cos(2x) = 2\left(-\frac{3}{5}\right)^2 - 1$ \\ $\cos(2x) = 2\left(\frac{9}{25}\right) - 1$ \\ $\cos(2x) = \frac{18}{25} - 1$ \\ $\cos(2x) = \frac{18}{25} - \frac{25}{25}$ \\ $\cos(2x) = -\frac{7}{25}$.[/tex]
Therefore, the value of [tex]$\cos(2x)$[/tex] = [tex]$ -\frac{7}{25}$[/tex].
what is the prime factorization for 37
The prime factorization of 37 is 37
We have,
The prime factorization of a number involves expressing it as a product of prime numbers.
However, in the case of prime numbers themselves, their prime factorization is simply the number itself.
In this case,
The number 37 is a prime number because it is only divisible by 1 and itself.
Since it has no other factors, its prime factorization is simply 37.
Thus,
The prime factorization of 37 is 37.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ6
what fraction 2/3 is found between which pair of fraction on the number line?
Solve the equation using the Zero-Product Property. –8n(10n – 1) = 0
Answer: The solution is,
[tex]n = 0\text{ or }n = \frac{1}{10}[/tex]
Step-by-step explanation:
Since, Zero product property states that if the product of two numbers or expression is equal to zero then either of the numbers or expressions must be equal to zero.
That is, If a.b = 0 ⇒ a = 0 or b = 0
Here, the given expression is,
[tex]-8n(10n-1)=0[/tex]
[tex]\implies (-8n)(10n-1)=0[/tex]
Thus, by the above property,
[tex]-8n = 0\text{ or }(10n-1)=0[/tex]
[tex]\implies n = \frac{0}{-8}\text{ or }10n= 1[/tex]
[tex]\implies n = 0\text{ or }n = \frac{1}{10}[/tex]
The equation of a line is y=3x+7. Change the equation so that it is proportional.
Answer:
y=3x
Step-by-step explanation:
For a line to be proportional it must have the form y=mx where the y-intercept is (0,0) through the origin. To change y=3x+7 to be proportional, write it as y=3x.
A theater can seat 864 people. The number of rows is 5 less than the number of seats in each row. How many rows of seats are there?
Final answer:
To determine the number of rows in a theater that can seat 864 people, with the number of rows being 5 less than the number of seats per row, we set up the equation x(x-5)=864. Solving this quadratic equation, we find that there are 31 rows of seats.
Explanation:
To solve for the number of rows in the theater, let's denote the number of seats in each row as x and the number of rows as x - 5. Since the product of the number of seats in each row and the number of rows will give us the total seating capacity, we can write down the equation:
x(x - 5) = 864
Expanding the equation, we get:
x2 - 5x - 864 = 0
Using the quadratic formula or factoring, we find that x = 36. Therefore:
The number of rows is x - 5 = 36 - 5 = 31.
So, the theater has 31 rows of seats.
Graph the line y+3=2(x-1) first identify the slope of the line
Find the prime factorization of the follwing numbers: (write p0 if a prime does not appear in the given number.)